German Offenlegungsschrift No. 2,402,606 describes a cooling body for disc-shaped semiconductors in which a cooling liquid flows through an axial bore of large diameter, via narrower connecting channels, into wafer-shaped recesses which lead up to the closing bottom of the semiconductor component and thus allow the latter to be cooled directly. From there, the cooling liquid flows through an annular channel located at the edge and an outlet bore radially outwards into a space surrounding the cooling body.